基于工序成本的多元过程能力指数分析

单一的多元过程能力指数在反映企业制造多元质量特性产品能力时存在缺陷,无法反映由于各工序成本的差异而造成的工序能力重要性的差别.基于此,从企业工序质量控制和工序成本关系的角度来分析,构建了基于工序成本修正的多元过程能力指数,反映企业的成本控制能力和产品竞争能力.最后,通过修正得到的多元过程能力指数,一方面优选企业的质量改进或控制方案,另一方面判定企业在同类产品制造中的实际质量控制能力和过程成本损失差异.     

Comparing Confidence Intervals for Multivariate Process Capability Indices

Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index C_p. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way. Copyright © 2011 John Wiley & Sons, Ltd.     

Multivariate Process Capability Index Based on Data Depth Concept

The purpose of this paper is to provide a multivariate process capability index, which could be used regardless on data distribution and also on data correlation. Such an index could be defined because of application of non‐parametric methodology that utilizes a data depth concept. Based on this concept, a two‐phase methodology was developed. In the first phase the modified tolerance region is estimated, while in the second one, a current process is assessed using the proposed three‐component index. Estimation of a modified tolerance region on the basis on historical data allows applying the methodology not only for bilateral quality characteristics but also for unilateral ones, where often in practice, the modified tolerance region could be defined as a closed region. The performance of the proposed index was evaluated using bilateral and unilateral examples. The obtained results showed that the proposed index performs satisfactorily for all the considered cases. Copyright © 2016 John Wiley & Sons, Ltd.     

Yield‐Based Capability Index for Evaluating the Performance of Multivariate Manufacturing Process

Process capability indices (PCIs) have been widely used in the manufacturing industry providing numerical measures on process precision, accuracy and performance. Capability indices measures for processes with a single characteristic have been investigated extensively. However, an industrial product may have more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, multivariate PCIs should be introduced. In this paper, we analyze the relationship between PCI and process yield. The PCI EC_pk is proposed based on the idea of six sigma strategy, and there is a one‐to‐one relationship between EC_pk index and process yield. Following the same, idea we propose a PCI MEC_pk to measure processes with multiple characteristics. MEC_pk index can evaluate the overall process yield of both one‐sided and two‐sided processes. We also analyze the effect of covariance matrix on overall process yield and suggest a solution for improving overall process yield. Copyright © 2013 John Wiley & Sons, Ltd.     

A New Multivariate Process Capability Index Under Both Unilateral and Bilateral Quality Characteristics

Process capability indices (PCIs) are used in statistical process control to evaluate the capability of the processes in satisfying the customer's needs. In the past two decades varieties of PCI are introduced by researchers to analyze the process capability with univariate or multivariate quality characteristics. To the best of our knowledge, most famous multivariate capability indices are proposed when the quality characteristics have both upper and lower specification limits. These indices are incapable to assess the multivariate processes capability with unilateral specification. In this article, we propose a new multivariate PCI to analyze the processes with one or more unilateral specification limits. This new index also accounts for all problems in the best PCIs of the literature. The performance of the proposed index is evaluated by real cases under different situations. The results show that the proposed index performs satisfactorily in all cases considered. Copyright © 2012 John Wiley & Sons, Ltd.     

An AR‐Sieve Bootstrap Control Chart for Autocorrelated Process Data

There are two major approaches in dealing with autocorrelated process data in process control, that is, residual‐based approaches and methods that modify control limits to adjust for autocorrelation. We proposed a methodology for constructing control charts for autocorrelated process data using the AR‐sieve bootstrap. The simulation study illustrates the relative advantage of the AR‐sieve bootstrap control chart with respect to the in‐control and out‐of‐control run length and false alarm rate. The proposed methodology works even for small sample sizes and conditions of the near nonstationarity of the generating process. The proposed AR‐sieve bootstrap control chart presents the advantage of being distribution‐free for certain class of linear models as well as the tracking of actual process observations instead of model residuals, thus facilitating the implementation during actual plant operations. Copyright © 2011 John Wiley & Sons, Ltd.     

基于粗糙集与四分位法的多元质量特性过程能力指数

多元质量特性过程能力指数的求解问题一直未得到很好的解决。本文简述了当前的研究现状,并利用粗糙集与四分位法,给出了计算多元质量特性过程能力指数的一种新方法,实例证明该方法是有效可行的。     

多元质量特性的过程能力指数

多元质量特性过程能力指数是一个尚未得到很好解决的问题。本文利用主成分分析，给出了计算多元质量特性过程能力指数的一种新方法，实证分析表明这种方法是可行的。     

Multivariate Process Capability Vector Based on One‐Sided Model

To evaluate the capability of manufacturing processes in satisfying the customer's needs, a variety of indices has been developed. Some of them are introduced by researchers to analyse the processes with multivariate quality characteristics. Most of the proposed in the literature multivariate capability indices are defined under assumption of normality distribution of the quality characteristics. Thus, the process region describing the variation of the data has an elliptical shape. In this paper, a multivariate process capability vector with three components is introduced, which allows to access the capability of a process with both normally and non‐normally quality characteristics due to application of a pair of one‐sided models as the process region shape. At the beginning, one‐sided models are defined, next the proposed vector components are proposed and the methodology of their evaluation is presented. The methodology (which in fact could be also applied to both the correlated and non‐correlated characteristics) is verified by applying simulation and real problems. The obtained results show that the proposed methodology performs satisfactorily in all considered cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Yield‐Related Process Capability Indices for Processes of Multiple Quality Characteristics

Process capability indices (PCIs) have been widely used in industries for assessing the capability of manufacturing processes. Castagliola and Castellanos (Quality Technology and Quantitative Management 2005, 2(2):201–220), viewing that there were no clear links between the definition of the existing multivariate PCIs and theoretical proportion of nonconforming product items, defined a bivariate C_pk and C_p (denoted by BC_pk and BC_p, respectively) based on the proportions of nonconforming product items over four convex polygons for bivariate normal processes with a rectangular specification region. In this paper, we extend their definitions to MC_pk and MC_p for multivariate normal processes with flexible specification regions. To link the index to the yield, we establish a ‘reachable’ lower bound for the process yield as a function of MC_pk. An algorithm suitable for such processes is developed to compute the natural estimate of MC_pk from process data. Furthermore, we construct via the bootstrap approach the lower confidence bound of MC_pk, a measure often used by producers for quality assurance to consumers. As for BC_p, we first modify the original definition with a simple preprocessing step to make BC_p scale‐invariant. A very efficient algorithm is developed for computing a natural estimator of BC_p. This new approach of BC_p can be easily extended to MC_p for multivariate processes. For BC_p, we further derive an approximate normal distribution for , which enables us to construct procedures for making statistical inferences about process capability based on data, including the hypothesis testing, confidence interval, and lower confidence bound. Finally, the proposed procedures are demonstrated with three real data sets. Copyright © 2012 John Wiley & Sons, Ltd.     

Functional Process Capability Indices for Circular Profile

Profile is a relation between one response variable and one or more explanatory variables that represent quality of a product or performance of a process. On the other hand, process capability indices are measures to help practitioners in improving the processes to satisfy the customer's expectations. Few researches are done to account for the process capability index in the areas of profile monitoring. All of these researches are focused on process capability index in simple linear profile. In all of these methods, response variables in different levels of explanatory variable are considered, and the relationship in all range of explanatory variable is neglected. In this paper, a functional method is proposed to measure process capability index of circular profiles in all range of explanatory variable. The proposed method follows the traditional definition of process capability indices. The functional method uses reference profile, functional specification limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability in each level of explanatory variable in circular profile as well as a unique value of process capability index for circular profile. The application of the proposed method is illustrated through a real case in automotive industry. Copyright © 2013 John Wiley & Sons, Ltd.     

A Multivariate Process Capability Index Based on the First Principal Component Only

Often the quality of a process is determined by several correlated univariate variables. In such cases, the considered quality characteristic should be treated as a vector. Several different multivariate process capability indices (MPCIs) have been developed for such a situation, but confidence intervals or tests have been derived for only a handful of these. In practice, the conclusion about process capability needs to be drawn from a random sample, making confidence intervals or tests for the MPCIs important. Principal component analysis (PCA) is a well‐known tool to use in multivariate situations. We present, under the assumption of multivariate normality, a new MPCI by applying PCA to a set of suitably transformed variables. We also propose a decision procedure, based on a test of this new index, to be used to decide whether a process can be claimed capable or not at a stated significance level. This new MPCI and its accompanying decision procedure avoid drawbacks found for previously published MPCIs with confidence intervals. By transforming the original variables, we need to consider the first principal component only. Hence, a multivariate situation can be converted into a familiar univariate process capability index. Furthermore, the proposed new MPCI has the property that if the index exceeds a given threshold value the probability of non‐conformance is bounded by a known value. Properties, like significance level and power, of the proposed decision procedure is evaluated through a simulation study in the two‐dimensional case. A comparative simulation study between our new MPCI and an MPCI previously suggested in the literature is also performed. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further. Copyright © 2012 John Wiley & Sons, Ltd.     

An Approach to Build Process‐Oriented Basis for Causation‐Based Multivariate SPC and Process Capability Analysis

Although various multivariate process monitoring techniques have been developed, they do not diagnose the process for finding the root causes of irregularities during production. There have been recent studies on a new method that involves process‐oriented basis representation, which links the process variation to its causes, and thus helps in monitoring and diagnosing a process. However, all the studies done so far focused on its application. In this paper, a method is proposed to build the process‐oriented basis for a process irrespective of the number of variables characterizing it. Along with various other statistical techniques, factor analysis and cluster analysis, with customized distance function, are used in developing the method. The built in process‐oriented basis is further used for multivariate statistical process control and process capability analysis. Multivariate solder‐paste problem from electronics industry is used for illustration. Copyright © 2012 John Wiley & Sons, Ltd.     

Process Capability Indices for Logistic Regression Profile

A profile is a relationship between a response variable and one or more independent variables that can describe the quality of a process or product. On the other side, for an in‐control process, capability indices are the criteria for process quality improvement that allows meeting customer expectations. Recently, evaluating the process capability of profiles has been investigated by some researchers. In all of these efforts, the response variable in the profile follows a normal distribution. However, sometimes, this assumption is violated, and the response variable may follow a binary or binomial distribution. In this paper, we propose two methods to measure the process capability when the quality of a process is characterized by a logistic regression profile. The performance of the proposed indices is evaluated through simulation studies. Finally, the application of the proposed methods is illustrated through a real case. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributional Properties of Multivariate Process Capability Indices under Normal and Non‐normal Distributions

Multivariate capability analysis has been the focus of study in recent years, during which many authors have proposed different multivariate capability indices. In the operative context, capability indices are used as measures of the ability of the process to operate according to specifications. Because the numerical value of the index is used to conclude about the capability of the process, it is essential to bear in mind that almost always that value is obtained from a sample of process units. Therefore, it is really necessary to know the properties that the indices have when they are calculated on sampling information, in order to assess the goodness of the inferences made from them. In this work, we conduct a simulation study to investigate distributional properties of two existing indices: NMCpm index based on ratio of volumes and Mp₂ index based on principal component analysis. We analyze the relative bias and the mean square error of the estimators of the indices, and we also obtain their empirical distributions that are used to estimate the probability that the indices classify correctly a process as capable or as incapable. The results allow us to recommend the use of one of these indices, as it has shown better properties. Copyright © 2016 John Wiley & Sons, Ltd.     

The New Nino Capability Index for Dynamic Process Capability Analysis

The process capability analysis is a crucial activity to evaluate if the process outcome meets the design specifications. Classically, such analysis is performed by verifying the in‐control condition of the process and evaluating suitable capability indices, by assuming the process in‐control steady‐state condition. However, the in‐control period of the process characterizes only a part of the system functioning cycle, the one with the lower defective rate. In particular, the system functioning cycle is also characterized by the out‐of‐control period, during which a greater defective rate is produced, and such increasing is not considered by the widely adopted capability indices. As consequence, the classical approaches to perform the process capability analysis involves an overestimation of the process capability level. For this reason, in order to overcome the previously described limitation, in the present paper it is proposed a new capability index based on the real defective rate of the process. Thus, such new index is able to estimate the real process capability level. Finally, in order to compare the new index to the conventional C_p capability index, a numerical comparison study related to a process capability analysis is carried out, and the related practical considerations are given. Copyright © 2013 John Wiley & Sons, Ltd.     

Multivariate process incapability vector

Process capability indices evaluate the capability of the processes in satisfying customer's requirements. This paper introduces a superstructure multivariate process incapability vector for multivariate normal processes and then, compares it with four recently proposed multivariate process capability indices to show its better performance. In addition, the effects of two modification factors are investigated. Also, bootstrap confidence intervals for the first component of the proposed vector are obtained. Furthermore, real manufacturing data sets are presented to demonstrate the applicability of the proposed vector.     

基于熵权和模糊物元的改进多元过程能力分析

为解决多品种小批量产品数据采集困难及各指标间存在交互影响致使传统方法难以奏效的现状,基于主成分分析法的多元过程能力指数会造成信息量缺损。该方法将工序能力影响因素采用模糊物元方法构造工序相似条件,选出相似工序将小批量问题变成大批量处理,应用公差系数法将原始数据转化为相对数据。提出基于熵权理论和模糊物元的改良多元过程能力指数。该论文结合某产品进行实例分析,验证了该方法的实用性和有效性。     

非正态过程能力指数研究中的几个问题

非正态分布条件下过程能力指数的研究是目前关于过程能力分析中的热点之一。针对该领域中存在的若干问题,分析了正态性假设的重要性,指出导致质量特性呈现非正态分布的原因及其后果,以及如何进行质量特性分布的一维和多维正态性检验。对非正态过程能力指数的估计方法进行了分析和归类,简要指出在非正态过程能力指数研究中需要继续深入的几个方向。